Approximation and Computation in Science and Engineering

Preface
Contents
Rearrangements, L-Superadditivity and Jensen-Type Inequalities
1 Introduction
2 L-Superadditivity Applications to Rearrangements
3 Jensen-Type Inequalities and Rearrangements
References
Approximate Generalized Jensen Mappings in 2-Banach Spaces
1 Introduction and Preliminaries
2 Main Results
3 Applications
References
The Asymptotic Expansion for a Class of Convergent Sequences Defined by Integrals
1 Introduction
2 Preliminaries
3 The Main Results
4 The Complete Asymptotic Expansion of Some Classical Sequences
4.1 The Sequence an=1-12+13-@汥瑀瑯步渠+(-1)(n-1)n
4.2 Other Expansion for an=1-12+13-@汥瑀瑯步渠+(-1)(n-1)n
4.3 The Sequence bn=1-13+15-@汥瑀瑯步渠+14n+1
4.4 The Sequence cn=1-11!+12-+@汥瑀瑯步渠+(-1)nn!
4.5 The Sequence en=1+11!+12!+@汥瑀瑯步渠+1n!
References
Weak Pseudoprimality Associated with the Generalized LucasSequences
1 Introduction
2 Some Pseudoprimality Properties
2.1 Classical Pseudoprimes Involving Generalized Lucas Sequences
2.2 Fibonacci and Bruckman–Lucas Pseudoprimes
2.3 Pell and Pell–Lucas Pseudoprimality
3 Generalized Bruckman–Lucas Pseudoprimes
3.1 Results for b=-1
3.2 Results for b=1
4 Weak Generalized Lucas Pseudoprimes
4.1 Results for b=-1
4.2 Results for b=1
5 Weak Generalized Lucas–Bruckner Pseudoprimes
5.1 Results for b=-1
5.2 Results for b=1
6 Conclusions and Future Work
References
Finite Shift-Invariant Subspaces of Periodic Functions: Characterization, Approximation, and Applications
1 Introduction
2 Shift-Invariant Frames for Subspaces of 2(IN)
3 Stable Reconstruction on Vϕ
4 Applications
Reference
Generalized Intensity-Dependent Multiphoton Jaynes–Cummings Model
1 Introduction
2 Time Evolution of the Atom Inversion Operator
3 Field Statistics of the Generalized Intensity-Dependent Multiphoton Jaynes–Cummings Model
4 Conclusions
References
Functional Inequalities for Multi-additive-Quadratic-Cubic Mappings
1 Introduction
2 Characterization of Multi-quadratic Mappings
3 Characterization of Multi-additive-Quadratic-Cubic Mappings
4 Stability of the Multi-additive-Quadratic-Cubic Mappings
5 Stability Results for (10) in Non-Archimedean Normed Spaces
References
Generalizations of Truncated M-Fractional Derivative Associated with (p,k)-Mittag-Leffler Function with Classical Properties
1 Introduction and Preliminaries
1.1 Special Cases
2 Truncated M-Fractional Derivative Type
3 Generalized M-Integral
4 Relation with Other Fractional Derivative Types
5 Application
5.1 Solution Heat Equation
5.1.1 Graphical and Numerical Results
5.2 Solution First-Order Differential Equation
6 Conclusion
References
On Hyers-Ulam-Rassias Stability of a Volterra-Hammerstein Functional Integral Equation
1 Introduction
2 Existence and Uniqueness
3 Hyers-Ulam-Rassias stability
References
Analysis of Electroencephalography (EEG) Signals Based on the Haar Wavelet Transformation
1 Introduction
2 Data Collection
3 The MCF Analysis
4 The Haar Wavelet Analysis: The Steps
5 The Results
6 Conclusions
References
Perov-Type Contractions
1 Introduction
2 Fixed Point Theorems of Perov Type on Generalized Metric Space
3 Perov Fixed Point Theorem on Cone Metric Spaces
4 Nonlinear Operatorial Contractions
5 Conclusion
References
On a Logarithmic Equation by Primes
1 Introduction and Main Result
2 Notations
3 Lemmas
4 Proof of the Theorem
References
Hermite-Hadamard Trapezoid and Mid-Point Divergences
1 Introduction
2 General Results
3 Related Results
4 Some Results for f-Divergences
5 Some Examples
References
Hermite-Hadamard-Type Integral Inequalities for PerspectiveFunction
1 Introduction
2 General Results
3 Double Integral Inequalities
4 Examples for Functions Defined on Rectangles
5 Examples for Functions Defined on Circular Sectors
References
On the Maximum Value of a Multi-variable Function
1 Introduction
2 Theorem 1 for the Case n=2
3 Proof of Theorem 1
Reference
Image Reconstruction for Positron Emission Tomography Based on Chebyshev Polynomials
1 Introduction
2 Mathematical Formulation
3 Spline Reconstruction
4 The Proposed Chebyshev Reconstruction Method
5 Numerical Implementation and Results
6 Conclusion
References
Approximation by Mixed Operators of Max-Product–Choquet Type
1 Introduction
2 Preliminaries on Choquet Integral
3 Approximation by Max-Product Kantorovich–Choquet-Type Operators
4 Approximation by Max-Product Discrete Singular Integrals of Choquet Type
5 Max-Product Kantorovich–Choquet Operators Based on (ϕ, ψ)-Kernels
References
On the Approximation of Extinction Time for the Discrete-Time Birth–Death Circuit Chains in Random Environments
1 Introduction
2 Circuit and Weight Representations of Discrete-Time Birth–Death Chains
2.1 Fixed Environments
2.2 Random Environments
3 The Mean Time to Extinction of the Discrete-Time Birth–Death Circuit Chains in Random Environments
3.1 For the Circuit Chain (Xn)nN
3.2 For the Circuit Chain (Xn)n
References
Some Hyperstability Results in Non-Archimedean 2-Banach Space for a σ-Jensen Functional Equation
1 Introduction
2 Background
3 A Fixed Point Theorem
4 Hyperstability of σ-Jensen Functional Equation in Non-archimedean 2-Banach Space
5 Applications
References
A Characterization for the Validity of the Hermite–Hadamard Inequality on a Simplex
1 Introduction, Motivation, and Problem Setting
2 Auxiliary Results
3 The Regular Case
4 Characterization Without Using Any Regularity Condition
5 Best Cubature Error Bounds
5.1 Characterization of the New Extended Cubature Formulas
6 Numerical Experiments
References
On the Stability of the Triangular Equilibrium Points in the Photogravitational R3BP with an Oblate Infinitesimal and Triaxial Primaries for the Binary Lalande 21258 System
1 Introduction
2 Equations of Motion
3 Location of the Triangular Points
4 Analysis of the Dynamics Around the Triangular Equilibrium Points
5 Numerical Simulation
6 Discussion and Conclusions
References
Normalized Symmetric Differential Operators in the Open Unit Disk
1 Introduction
2 Methodology
2.1 Symmetric Differential Operators (SDO)
3 Results
4 Applications
5 Conclusion
References
New Hermite–Hadamard Inequalities Concerning Twice Differentiable Generalized ψ-Convex Mappings via Conformable Fractional Integrals
1 Introduction
2 Main Results
3 Applications to Special Means
References
Some New Fractional Inequalities Using n-Polynomials s-TypeConvexity
1 Introduction
2 Hermite–Hadamard Inequalities for n-Polynomial s-Type Convex Functions
3 Ostrowski Type Inequalities for Differentiable Functions
4 Other Results About Ostrowski Type Inequalities for Twice Differentiable Functions
5 Corollaries
References
Hyperstability of Orthogonally 3-Lie Homomorphism: An Orthogonally Fixed Point Approach
1 Introduction
2 Main Results
References
Some New Inequalities for Fractional Integral Operators
1 Introduction
2 Generalized Fractional Integral Operators and Fractional Area Balance Operators
3 Some Inequalities for T19
4 Some Inequalities for Operator T14
References
New Generalized Convexity and Their Applications
1 Introduction
2 Generalized Convexity in Normed Linear Spaces
3 Generalized Ostrowski Type Inequalities
4 Proofs of Theorems 7 and 8
5 Perturbed Simpson Type Inequalities and Approximations
References
Ternary Biderivations and Ternary Bihomorphisms in C*-Ternary Algebras
1 Introduction and Preliminaries
2 Ternary Bihomomorphisms in C*-Ternary Algebras
3 Ternary Biderivations on C*-Ternary Algebras Associated with the Bi-additive Functional Inequality (1)
4 Ternary Bihomomorphisms in C*-Ternary Algebras Associated with the Bi-additive Functional Inequality (1)
References
Hyers–Ulam Stability of an Additive-Quadratic Functional Equation
1 Introduction and Preliminaries
2 Hyers–Ulam Stability of Lie biderivations on Lie Banach Algebras: Direct Method
3 Hyers–Ulam Stability of Lie Bihomomorphisms in Lie Banach Algebras: Direct Method
4 Hyers–Ulam Stability of Lie Biderivations on Lie Banach Algebras: Fixed Point Method
5 Hyers–Ulam Stability of Lie Bihomomorphisms in Lie Banach Algebras: Fixed Point Method
6 Conclusions
References
Orthogonal Dirichlet Polynomials
1 Introduction
2 The Arctangent Density
3 Laguerre Weight
4 Rational Weights
5 Legendre Weight
6 Conclusions
References
Generalizations and Improvements of Approximations of Some Analytic Functions: A Survey
1 Introduction
2 Refinements and Generalizations of Some Inequalities Involving Inverse Trigonometric Functions
2.1 Shafer–Fink's Type Inequalities
2.2 Shafer's Type Inequalities
3 Inequalities Containing the Sinc Function
3.1 Inequalities Related to Wilker–Cusa–Huygens's Inequalities
3.2 Some Exponential Inequalities Related to the Sinc Function
3.3 Wilker's Type Inequalities
4 Generalizations and Improvements of Some Inequalities Using the Double-Sided Taylor's Approximations
5 Conclusion
References
Some Classes of Meir–Keeler Contractions
1 Introduction
2 Z-Contractions Are Meir–Keeler Contractions
3 Weakly Type Contractions Are Meir–Keeler Contractions
4 F-Contractions and Meir–Keeler Contractions
References
Interpolation of the Zech's Logarithm: Explicit Forms
1 Introduction
2 Lagrange and Exponential Interpolation
3 Main Computations
4 Examples
5 Conclusions
References
Numerical Calculations on Multi-Photon Processes in Alkali Metal Vapors
1 Introduction
2 Theoretical Modeling and Approximations
3 Results and Discussion
4 Conclusions
References
General Preinvex Functions and Variational-Like Inequalities
1 Introduction
2 Preliminary Results
3 Main Results
4 Applications
5 General Variational-Like Inequalities
References
A Variational Formulation of Network Games with Random Utility Functions
1 Introduction
2 Network Game Classes and Variational Inequality Approach
3 The Random Linear-Quadratic Model
4 Numerical Experiments
5 Conclusions and Future Research Directions
References
Fixed Point Theory in Graph Metric Spaces
1 Introduction
2 Preliminaries
3 Main Results
References
Approximate Solution of Fredholm Integral and Integro-Differential Equations with Non-Separable Kernels
1 Introduction
2 Direct Matrix Methods
3 Approximate Solution of Integral Equations with Non-Separable Kernels
4 Approximate Solution of Integro-Differential Equations with Non-Separable Kernels
5 Conclusions
References
Ordinary, Super and Hyper Relators Can Be Used To Treat the Various Generalized Open Sets in a Unified Way
1 Motivations
2 Preliminaries
3 A Few Basic Facts on Relations
4 Some Basic Properties of Super Relations
5 Relationships Between Ordinary and Super Relations
6 Further Theorems on the Operations , and
7 Relationally Defined Inverses of Super Relations
8 Functionally and Relationally Defined Compositions of Super Relations
9 The Duals of Super and Hyper Relations
10 A Few Basic Facts on Relators
11 Structures Derived from Super Relators
12 Basic Theorems on the Small Closure and Interior
13 Basic Theorems on Fat and Dense Sets
14 Further Structures Derived from Super Relators
15 Basic Theorems on Topologically Open Sets
16 Structures Derived from the Super Relator U
17 Structures Derived from Ordinary Relators
18 Further Theorems on Small Closures and Interiors
19 Further Theorems on Fat and Dense Sets
20 Further Structures Derived from Ordinary Relators
21 Further Theorems on Open and Fat Sets
22 Reflexive, Non-Partial and Non-Degenerated Relators
23 Topological and Quasi-Topological Relators
24 A Few Basic Facts on Filtered Relators
25 A Few Basic Facts on Quasi-Filtered Relators
26 Some Further Theorems on Topologically Filtered Relators
27 Some More Particular Theorems on Topologically Filtered Relators
28 Proximally Closed Sets in Super Relator Spaces
29 Two Further Illustrative Examples and Two Further General Theorems
30 Some Set-Theoretic Properties of the Families τto-U and τto-U
31 Topological Closures of Families of Sets
32 Some Basic Properties of the Operations k and
33 Some Set-Theoretic Properties of the Families A and Bk
34 A Weak Intersection Property of the Families Ak and A
35 Some Further Theorems on the Operations and k
36 A Further Theorem on Proximally Closed Sets
References
Applications of Apostol-type Numbers and Polynomials: Approach to Techniques of Computation Algorithms in Approximation and Interpolation Functions
1 Preliminaries
2 Apostol-Type Numbers and Polynomials with Their Properties and Relations
3 Identities and Derivative Formulas Arising from the Partial Differential Equations Including the Generating Functions for the Numbers Wn( k) (λ) and the Polynomials Wn( k) (x;λ)
4 Relations Among the Numbers Wn(k)(λ), the Polynomials Wn(k)(x;λ) and Other Well-Known Apostol-Type Special Numbers and Polynomials
4.1 Relations of the Numbers Wn(k)(λ) and the Polynomials Wn(k)(x;λ) with the Apostol-Bernoulli Numbers and Polynomials of Higher Order
4.2 Relations of the Numbers Wn(k)(λ) and the Polynomials Wn(k)(x;λ) with the Apostol-Euler Numbers and Polynomials of Higher Order
4.3 Relations of the Numbers Wn(k)(λ) and the Polynomials Wn(k)(x;λ) with the Apostol-Genocchi Numbers and Polynomials of Higher Order
4.4 Relations of the Numbers Wn(k)(λ) and the Polynomials Wn(k)(x;λ) with the Frobenius-Euler Numbers and Polynomials of Higher Order
4.5 Relations of the Numbers Wn(k)(λ) and the Polynomials Wn(k)(x;λ) with the λ-array Polynomials, the λ-Stirling Numbers, and λ-Bernoulli Numbers and Polynomials
5 Application of the Laplace Transform and Mellin Transformation to the Generating Function of Apostol-Type Polynomials and λ-array Polynomials
5.1 Application of the Laplace Transform to the Generating Function for the Apostol-Type Polynomials Wn( k) (x;λ) and Array Type Polynomials
6 Application of the Mellin Transformation to the Generating Function for the Apostol-Type Numbers Wn(λ), the Numbers Wn(k)(λ), and the Polynomials Wn( k)(x;λ)
6.1 Interpolation Function Related to the Families of Zeta-Type Functions
6.2 Interpolation Function for the Apostol-Type Numbers Wn(λ)
6.3 Interpolation Functions for the Numbers Wn(k)(λ) and the Polynomials Wn( k) (x;λ)
7 Functional Equations and Their Associated Raabe-Type Multiplication Formula for the Polynomials Wn( k) (x;λ)
8 Some Special Power Series Including the Numbers of the Lyndon Words and Binomial Coefficients
9 Computational Algorithms Arising from the Recurrence Formula for the Numbers Wn(k)(λ)
10 Illustrations and Observations on Approximations of the Functions G( λ,p,k) by the Rational Functions Wn( k) (λ)
11 Further Remarks and Observation on the Bernstein Polynomials and Their Approximations
References
Spectra of Signed Graphs
1 Introduction and Preliminaries
2 Adjacency Matrix of Signed Graphs
3 Laplacian Spectra of Signed Graphs
3.1 Largest Laplacian Eigenvalue
3.2 Least Laplacian Eigenvalue
4 Spectra and Signed Graph Structure
4.1 Paths and Cycles
4.2 Signed Unicyclic Graphs
4.3 Signed Graphs with Two Distinct Eigenvalues
4.4 Graphs with Symmetric Spectrum
References
Perturbed Geometric Contractions in Ordered Metric Spaces
1 Introduction
2 Dependent Choice Principles
3 Conv-Cauchy Structures
4 Meir–Keeler Relations
5 Statement of the Problem
6 Main Result
7 Particular Cases
References
On G(σ,h)-Convexity of the Functions and Applications to Hermite-Hadamard's Inequality
1 Introduction and Preliminaries
2 Results and Discussions
2.1 G(σ,h)-Convexity
2.2 Strongly G(σ,h)-Convexity
References